Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Transitivity of codimension-one Anosov actions of R(k) on closed manifolds

We consider Anosov actions of R(k), k >= 2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of R(k) has dimension one. We prove that if the ambient manifold has dimension greater than k + 2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

Foliations and polynomial diffeomorphisms of R(3)

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of {f, g, h}, made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek`s Jacobian Conjecture for polynomial maps of R(n).

Emplacement mechanism of the main granite pluton of the Lavras do Sul intrusive complex, South Brazil, determined by magnetic anisotropies

Magnetic fabric and rock magnetism studies were performed on apparently isotropic granite facies from the main intrusion of the Lavras do Sul Intrusive Complex pluton (LSIC, Rio Grande do Sul, South Brazil). This intrusion is roughly circular (similar to 12 x 13.5 km), composed of alkali-calcic and alkaline granitoids, with the latter occupying the margin of the pluton. Magnetic fabrics were determined by applying both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The two fabrics are coaxial. The parallelism between AMS and AARM tensors excludes the presence of a single domain (SD) effect on the AMS fabric of the granites. Several rock-magnetism experiments performed in one specimen from each sampled site show that for all sites the magnetic susceptibility is dominantly carried by ferromagnetic minerals, while mainly magnetite carries the magnetic fabrics. Lineations and foliations in the granite facies were successful determined by applying magnetic methods. Magnetic lineations are gently plunging and roughly parallel to the boundaries of the pluton facies, except at the few sites in the central facies which have a radial orientation pattern. In contrast, the magnetic foliations tend to follow the contacts between the different granite facies. They are gently outerward-dipping inside the pluton, and become either steeply southwesterly dipping or vertical towards its margin. The lack of solid-state and subsolidus deformations at outcrop scale and in thin sections precludes deformation after full crystallization of the pluton. This evidence allows us to interpret the observed magnetic fabrics as primary in origin (magmatic) acquired when the rocks were solidified as a result of processes reflecting magma flow. The foliation pattern displays a dome-shaped form for the main LSIC-pluton. However, the alkaline granites which outcrop in the southern part of the studied area have an inward-dipping foliation, and the steeply plunging magnetic lineation suggests that this area could be part of a feeder zone. The magma ascent probably occurred due to ring-diking. (C) 2008 Elsevier B.V. All rights reserved.

Tectonic fabric revealed by AARM of the proterozoic mafic dike swarm in the Salvador city (Bahia state): Sao Francisco Craton, NE Brazil

Magnetic fabric and rock magnetism studies were performed on 25 unmetamorphosed mafic dikes of the Meso-Late Proterozoic (similar to 1.02 Ga) dike swarm from Salvador (Bahia State, NE Brazil). This area lies in the north-eastern part of the Sao Francisco Craton, which was dominantly formed/reworked during the Transamazonian orogeny (2.14-1.94 Ga). The dikes crop out along the beaches and in quarries around Salvador city, and cut across both amphibolite dikes and granulites. Their widths range from a few centimeters up to 30 m with an average of similar to 4 m, and show two main trends N 140-190 and N 100-120 with vertical dips. Magnetic fabrics were determined using both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The magnetic mineralogy was investigated by many experiments including remanent magnetization measurements at variable low temperatures (10-300 K), Mossbauer spectroscopy, high temperature magnetization curves (25-700 degrees C) and scanning electron microscopy (SEM). The rock magnetism study suggests pseudo-single-domain magnetite grains carrying the bulk magnetic susceptibility and AARM fabrics. The magnetite grains found in these dikes are large and we discard the presence of single-domain grains. Its composition is close to stoichiometric with low Ti substitution, and its Verwey transition occurs around 120 K. The main AMS fabric recognized in the swarm is so-called normal, in which the K(max)-K(int) plane is parallel to the dike plane and the magnetic foliation pole K(min)) is perpendicular to it. This fabric is interpreted as due to magma flow, and analysis of the K m inclination permitted to infer that approximately 80% of the dikes were fed by horizontal or sub-horizontal flows (K(max) < 30 degrees). This interpretation is supported by structural field evidence found in five dikes. In addition, based on the plunge of K(max), two mantle sources could be inferred; one of them which fed about 80% of the swarm would be located in the southern part of the region, and the other underlied the Valeria quarry. However, for all dikes the AARM tensors are not coaxial with AMS fabrics and show a magnetic lineation (AARM(max)) oriented to N30-60E, suggesting that magnetite grains were rotated clockwise from dike plane. The orientation of AARM lineation is similar to the orientation of a system of faults in which the Salvador normal fault is the most important. These faults were formed during Cretaceous rifting in the Reconcavo-Tucano-jatoba assemblage that corresponds to an aborted intra-continental rift formed during the opening of the South Atlantic. Therefore, the AARM fabric found for the Salvador dikes is probably tectonic in origin and suggests that the dike swarm was affected by the important tectonic event responsible for the break-up of the Gondwanaland. (C) 2008 Elsevier B.V. All rights reserved.

Conflicting structural and geochronological data from the Ibituruna quartz-syenite (SE Brazil): Effect of protracted ""hot"" orogeny and slow cooling rate?

The Ibituruna quartz-syenite was emplaced as a sill in the Ribeira-Aracuai Neoproterozoic belt (Southeastern Brazil) during the last stages of the Gondwana supercontinent amalgamation. We have measured the Anisotropy of Magnetic Susceptibility (AMS) in samples from the Ibituruna sill to unravel its magnetic fabric that is regarded as a proxy for its magmatic fabric. A large magnetic anisotropy, dominantly due to magnetite, and a consistent magnetic fabric have been determined over the entire Ibituruna massif. The magmatic foliation and lineation are strikingly parallel to the solid-state mylonitic foliation and lineation measured in the country-rock. Altogether, these observations suggest that the Ibituruna sill was emplaced during the high temperature (similar to 750 degrees C) regional deformation and was deformed before full solidification coherently with its country-rock. Unexpectedly, geochronological data suggest a rather different conclusion. LA-ICP-MS and SHRIMP ages of zircons from the Ibituruna quartz-syenite are in the range 530-535 Ma and LA-ICP-MS ages of zircons and monazites from synkinematic leucocratic veins in the country-rocks suggest a crystallization at similar to 570-580 Ma, i.e., an HT deformation >35My older than the emplacement of the Ibituruna quartz-syenite. Conclusions from the structural and the geochronological studies are therefore conflicting. A possible explanation arises from (40)Ar-(39)Ar thermochronology. We have dated amphiboles from the quartz-syenite, and amphiboles and biotites from the country-rock. Together with the ages of monazites and zircons in the country-rock, (40)Ar-(39)Ar mineral ages suggest a very low cooling rate: <3 degrees C/My between 570 and similar to 500 Ma and similar to 5 degrees C/My between 500 and 460 Ma. Assuming a protracted regional deformation consistent over tens of My, under such stable thermal conditions the fabric and microstructure of deformed rocks may remain almost unchanged even if they underwent and recorded strain pulses separated by long periods of time. This may be a characteristic of slow cooling ""hot orogens"" that rocks deformed at significantly different periods during the orogeny, but under roughly unchanged temperature conditions, may display almost indiscernible microstructure and fabric. (C) 2009 Elsevier B.V. All rights reserved.

Lower and Upper Neoproterozoic magmatic records in Itaiacoca Belt (Parana-Brazil): Zircon ages and lithostratigraphy studies

The Itaiacoca Belt is a sequence of metavolcanic and metasedimentary rocks that crop out east of Parana and southeast of Sao Paulo states, in southern Brazil. This geologic-geochronologic study supports division of the Itaiacoca Belt into two major lithologic sequences. The older is a carbonate platform sequence (dolomitic meta-limestones/metamarls/calc-phyllites/ carbonate phyllites) with minimum deposition ages related to the end of the Mesoproterozoic/beginning of the Neoproterozoic (1030-908 Ma:U-Pb, zircon of metabasic rocks). The younger sequence contains mainly clastics deposits (meta-arkoses/metavolcanics/metaconglomerates/metapelites) with deposition ages related to the Neoproterozoic (645-628 Ma:U-Pb,zircon of metavolcanic rocks). These ages are quite close to K-Ar ages (fine fraction) of the 628-610 Ma interval, associated with metamorphism and cooling of the Itaiacoca Belt. The contact between the dolomitic meta-limestones and meta-arkoses is marked by intense stretching and high-angle foliation, suggesting that the discontinuity between these associations resulted from shearing. It is proposed here that the term Itaiacoca Sequence, should represent the dolomitic meta-limestones, and the term Abapa Sequence represents the meta-arkoses/metavolcanics/phyllites. in a major tectonic context, these periods are related to the break-up of Rodinia Supercontinent (1030-908 Ma) and the amalgamation of the Gondwana Supercontinent (645-628 Ma). (C) 2008 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.